Nuprl Lemma : pv11_p1_add_if_new_if
∀Cmd:ValueAllType. ∀p:ℤ × Cmd. ∀proposals:(ℤ × Cmd) List.
((¬↑(pv11_p1_in_domain(Cmd) (fst(p)) proposals)) ⇒ (p ∈ pv11_p1_add_if_new() pv11_p1_same_proposal(Cmd) p proposals))
Proof
Definitions occuring in Statement :
pv11_p1_add_if_new: pv11_p1_add_if_new(),
pv11_p1_same_proposal: pv11_p1_same_proposal(Cmd),
pv11_p1_in_domain: pv11_p1_in_domain(Cmd),
l_member: (x ∈ l),
list: T List,
vatype: ValueAllType,
assert: ↑b,
pi1: fst(t),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
vatype: ValueAllType,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
guard: {T},
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
ifthenelse: if b then t else f fi ,
not: ¬A,
exists: ∃x:A. B[x],
pv11_p1_in_domain: pv11_p1_in_domain(Cmd),
pi1: fst(t),
pv11_p1_same_proposal: pv11_p1_same_proposal(Cmd),
rev_implies: P ⇐ Q,
cand: A c∧ B,
false: False,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Latex:
\mforall{}Cmd:ValueAllType. \mforall{}p:\mBbbZ{} \mtimes{} Cmd. \mforall{}proposals:(\mBbbZ{} \mtimes{} Cmd) List.
((\mneg{}\muparrow{}(pv11\_p1\_in\_domain(Cmd) (fst(p)) proposals))
{}\mRightarrow{} (p \mmember{} pv11\_p1\_add\_if\_new() pv11\_p1\_same\_proposal(Cmd) p proposals))
Date html generated:
2016_05_17-PM-03_16_33
Last ObjectModification:
2015_12_29-PM-11_20_42
Theory : paxos!synod
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